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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 44, page id 824573315:0064
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CAP. 12.
8dF.) AC, hoc concelto,
mulcomagis dicendum et
sec duas peripherias NA
AE, angulum concinere; eAt
enim curvacura N a F du-
PIa CUIEVETUTX T A P. ouod
si N A P non sIc angulus,
Sed una linea concinuata (-
re in dircetum posica (prout
concedi Colet ab omnibus;
quis enim dixeric in singulis
Peripherixe punctisangulum
Formari :) neq; erie T AF vel P A N angulus, led pocius li-
nea in directum potica; Et conlequenter neq; P A P. aUE T A N
ansulus eric, led porius linex coincidences, quantum (cilicet ad
iplum punctum concactas acrinet.
Rcg; hinc obicer dilcere licer, quo pacto dux dissimiles linex.
Duca cuera _ recta, vel peripheria e parabola, vel eciam perio
pheria majoris deminoris circuli, aut etiam conrexa _ conca-
ra. REc. concinuori polsinc. Onod monvisse lufticit.
60 Nocum ekt, aream ligura regularis quorcunq; lacerum
aequalem esse rectansulo quod semiperimeero de rectâ a CentrO
ad perimeerum perpendiculari concinecur; (En recta illa non
Ec ad perimcerum perpendicularis, Peu ad angulos rectos, se
cus erie,) AE idem ostendic Archimedes, (prop.r. de dimen.
sione circuli,) de circulo; nempe arcam circuli aequalem else
rectangulo sub racio ex lemiperipheria; P. A igicur cadius ad pe-
ripheriam perpendicularis, sive ad angulos rectos. Si enim an-
fulus radio ee pesipheria comprehentus, minor esser recto rectin
lineo; elec area circuliminor quam ejulmodi parallelogram
mum rectangulum. Nams illud quidem univerlalicer rerum eAt;
si duae rectx, quarum altera cs Cemiperimecer hgura regularis,
alcera recta ad lacus iplins quodlibet quocunq; angulo ducta
parallelogrammums eodem angulo concincane, erie hoc paral-
selogrammium arex ictius tgurx regularis aequale, (uc probari
Pocekt ex 35C 1.) Cum isitur parallelogrammum racio (hOC
B, recta a cenero) e semiperipheria comprehentum, quod a-
L
De anculo contactus.
neq; erune lis ex TA, AF, auE P R, A N, in directum pOHICX.
nam linea in directum policx non concinene angulum, per